Background

This analysis document compliments FIA NLS Models: Biomass vs. Stand Age, G-Reconciled. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.

Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)

Below the model fitting procedure is implemented by ecoprovince:

Analysis 1: Temporally-balanced analysis

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   4834     1203.6                                 
## 2   4833     1198.4  1   5.229  21.087 4.501e-06 ***
## 3   4797     1065.9 36 132.536  16.569 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 52557.62
## 2     2 52538.57
## 3     3 51686.29
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    9.371e-02  1.584e-01   0.592    0.554    
## phi   2.189e-02  5.164e-03   4.238  2.3e-05 ***
## alpha 8.574e-01  3.453e-02  24.834  < 2e-16 ***
## A     4.720e+02  3.492e+01  13.516  < 2e-16 ***
## k     1.913e+02  1.634e+01  11.711  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4714 on 4797 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.677e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
##   model      AIC
## 1     3 51686.29
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    9.371e-02  1.584e-01   0.592    0.554    
## phi   2.189e-02  5.164e-03   4.238  2.3e-05 ***
## alpha 8.574e-01  3.453e-02  24.834  < 2e-16 ***
## A     4.720e+02  3.492e+01  13.516  < 2e-16 ***
## k     1.913e+02  1.634e+01  11.711  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4714 on 4797 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.677e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   4832     1179.6                                 
## 2   4831     1174.7  1   4.831  19.865 8.498e-06 ***
## 3   4795     1032.2 36 142.553  18.395 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 51686.29
## 2     4 52463.90
## 3     5 52446.05
## 4     6 51536.04
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.878e-01  1.695e-01   1.697   0.0897 .  
## phi   2.131e-02  5.077e-03   4.196 2.76e-05 ***
## alpha 8.507e-01  3.272e-02  26.000  < 2e-16 ***
## a     4.187e+01  1.985e+00  21.095  < 2e-16 ***
## b     1.144e+02  5.296e+00  21.609  < 2e-16 ***
## c     1.120e+02  4.466e+00  25.077  < 2e-16 ***
## d     8.929e-01  4.338e-02  20.584  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.464 on 4795 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (36 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98555, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -28.349, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df  Sum Sq F value    Pr(>F)    
## 1  12943     5165.4                                   
## 2  12940     5159.8    3    5.58  4.6656  0.002919 ** 
## 3   9751     3578.8 3189 1580.98  1.3508 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 135621.4
## 2     2 135589.0
## 3     3 102097.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.004e-01  1.380e-01   0.727    0.467    
## phi   1.684e-02  4.183e-03   4.025 5.75e-05 ***
## alpha 7.029e-01  3.058e-02  22.986  < 2e-16 ***
## A     1.838e+02  7.218e+00  25.468  < 2e-16 ***
## k     6.575e+01  2.774e+00  23.697  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6058 on 9751 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.023e-07
##   (3206 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9751     3578.8                                
## 2   9750     3513.0  1 65.778  182.56 < 2.2e-16 ***
## 3   9749     3429.0  1 84.031  238.91 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 102097.9
## 2    3a 101918.9
## 3    3b       NA
## 4    3c 101684.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.104e-01  1.419e-01   1.483    0.138    
## phi   1.639e-02  4.063e-03   4.035 5.51e-05 ***
## alpha 7.874e-01  2.024e-02  38.905  < 2e-16 ***
## A     1.239e+02  5.343e+00  23.190  < 2e-16 ***
## k     4.647e+01  1.612e+00  28.823  < 2e-16 ***
## p     1.969e-01  9.864e-03  19.957  < 2e-16 ***
## s     2.352e+00  1.344e-01  17.501  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5931 on 9749 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 7.594e-06
##   (3206 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df  Sum Sq F value    Pr(>F)    
## 1  12941     5088.9                                   
## 2  12938     5084.0    3    4.95  4.2015  0.005589 ** 
## 3   9749     3417.4 3189 1666.61  1.4909 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 101684.7
## 2     4 135432.3
## 3     5 135401.4
## 4     6 101651.5
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.376e-01  1.431e-01   1.660   0.0969 .  
## phi   1.578e-02  4.052e-03   3.895  9.9e-05 ***
## alpha 7.920e-01  1.982e-02  39.963  < 2e-16 ***
## a     2.495e+01  9.866e-01  25.290  < 2e-16 ***
## b     8.618e+01  3.346e+00  25.756  < 2e-16 ***
## c     1.193e+02  5.396e+00  22.110  < 2e-16 ***
## d     1.250e+00  4.543e-02  27.525  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5921 on 9749 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3206 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   5442     948.80                             
## 2   5441     948.80  1   0.00  0.0001  0.993    
## 3   5404     844.42 37 104.37 18.0528 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 59550.63
## 2     2 59552.63
## 3     3 58626.28
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     1.841e-01  1.319e-01   1.396    0.163    
## phi   -3.225e-04  4.033e-03  -0.080    0.936    
## alpha  8.131e-01  3.087e-02  26.339   <2e-16 ***
## A      4.751e+02  2.821e+01  16.842   <2e-16 ***
## k      1.446e+02  1.008e+01  14.350   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3953 on 5404 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.791e-06
##   (37 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   5404     844.42                          
## 2   5403     844.30  1 0.11944  0.7643  0.382
##   model      AIC
## 1     3 58626.28
## 2    3a 58627.52
## 3    3b 58613.23
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     2.351e-01  1.354e-01   1.737   0.0825 .  
## phi   -9.045e-04  4.026e-03  -0.225   0.8223    
## alpha  8.196e-01  3.110e-02  26.350  < 2e-16 ***
## A      3.171e+02  2.750e+01  11.529  < 2e-16 ***
## k      7.266e+01  9.286e+00   7.825 6.05e-15 ***
## s      1.229e+00  6.088e-02  20.184  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3948 on 5403 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.512e-06
##   (37 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   5440     940.37                             
## 2   5439     940.37  1   0.00   0.000      1    
## 3   5402     834.50 37 105.87  18.522 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 58613.23
## 2     4 59506.03
## 3     5 59508.03
## 4     6 58566.32
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.336e-01  1.346e-01   1.735   0.0828 .  
## phi   0.000e+00  4.011e-03   0.000   1.0000    
## alpha 8.141e-01  2.994e-02  27.186   <2e-16 ***
## a     2.993e+01  2.754e+00  10.868   <2e-16 ***
## b     1.665e+02  9.167e+00  18.167   <2e-16 ***
## c     1.428e+02  1.222e+01  11.687   <2e-16 ***
## d     1.375e+00  8.077e-02  17.026   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.393 on 5402 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (37 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   3547     1178.6                                 
## 2   3546     1173.8   1   4.76 14.3834 0.0001516 ***
## 3   2736      837.3 810 336.54  1.3577 1.349e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 38157.03
## 2     2 38144.66
## 3     3 29468.73
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.49696    0.20575  -2.415 0.015785 *  
## phi     0.04216    0.01152   3.660 0.000257 ***
## alpha   0.82305    0.05521  14.908  < 2e-16 ***
## A     510.07403   59.25009   8.609  < 2e-16 ***
## k     204.81027   26.87562   7.621 3.46e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5532 on 2736 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.721e-06
##   (811 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   2736     837.30                         
## 2   2735     836.95  1  0.345  1.1274 0.2884
##   model      AIC
## 1     3 29468.73
## 2    3a 29469.60
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.49696    0.20575  -2.415 0.015785 *  
## phi     0.04216    0.01152   3.660 0.000257 ***
## alpha   0.82305    0.05521  14.908  < 2e-16 ***
## A     510.07403   59.25009   8.609  < 2e-16 ***
## k     204.81027   26.87562   7.621 3.46e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5532 on 2736 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.721e-06
##   (811 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   3545    1160.08                                 
## 2   3544    1155.44   1   4.64 14.2326 0.0001642 ***
## 3   2734     811.87 810 343.57  1.4284 3.814e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 29468.73
## 2     4 38104.80
## 3     5 38092.57
## 4     6 29388.21
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.39139    0.21414  -1.828 0.067694 .  
## phi     0.04407    0.01139   3.870 0.000111 ***
## alpha   0.84560    0.04743  17.827  < 2e-16 ***
## a      28.12536    2.22465  12.643  < 2e-16 ***
## b     125.18955    7.61599  16.438  < 2e-16 ***
## c     104.14395    6.01856  17.304  < 2e-16 ***
## d       1.01334    0.06134  16.520  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5449 on 2734 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (811 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95927, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.002, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df  Sum Sq F value    Pr(>F)    
## 1   6383    1208.62                                   
## 2   6382    1205.07    1   3.549 18.7934 1.479e-05 ***
## 3   5253     959.89 1129 245.185  1.1885 7.222e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66739.63
## 2     2 66722.85
## 3     3 54960.87
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.076148   0.122692  -0.621  0.53486    
## phi    -0.017140   0.005541  -3.093  0.00199 ** 
## alpha   0.752631   0.033877  22.217  < 2e-16 ***
## A     274.803374  12.815771  21.443  < 2e-16 ***
## k      76.174549   4.734840  16.088  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4275 on 5253 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.076e-07
##   (1130 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   5253     959.89                           
## 2   5252     959.83  1 0.055076  0.3014 0.5831
##   model      AIC
## 1     3 54960.87
## 2    3a 54962.57
## 3    3b 54936.56
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.046206   0.124285  -0.372  0.71007    
## phi    -0.017210   0.005522  -3.117  0.00184 ** 
## alpha   0.761109   0.034070  22.340  < 2e-16 ***
## A     192.955583  11.041778  17.475  < 2e-16 ***
## k      40.235430   3.159348  12.735  < 2e-16 ***
## s       1.392459   0.078233  17.799  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4264 on 5252 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.199e-06
##   (1130 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   6381    1195.86                                  
## 2   6380    1195.86    1   0.00  0.0000         1    
## 3   5251     944.25 1129 251.61  1.2393 1.062e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 54936.56
## 2     4 66675.81
## 3     5 66677.81
## 4     6 54878.47
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.19990    0.11554   -1.73   0.0837 .  
## phi     0.00000    0.00566    0.00   1.0000    
## alpha   0.76139    0.03295   23.11   <2e-16 ***
## a      31.44045    2.91648   10.78   <2e-16 ***
## b     117.40902    5.20293   22.57   <2e-16 ***
## c     106.43496    6.07343   17.52   <2e-16 ***
## d       1.26371    0.07424   17.02   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4241 on 5251 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1130 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)    
## 1   7773     2698.5                               
## 2   7772     2698.1   1   0.388  1.1185 0.2903    
## 3   7640     2402.6 132 295.453  7.1174 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85845.56
## 2     2 85846.44
## 3     3 84005.02
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.306518   0.177137   7.376 1.81e-13 ***
## phi    -0.005339   0.004923  -1.084    0.278    
## alpha   0.615720   0.024140  25.506  < 2e-16 ***
## A     223.187781   9.171669  24.334  < 2e-16 ***
## k      51.702124   2.145762  24.095  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5608 on 7640 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.623e-06
##   (145 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7640     2402.6                                
## 2   7639     2305.2  1  97.44  322.90 < 2.2e-16 ***
## 3   7638     2248.0  1  57.17  194.24 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 84005.02
## 2    3a 83690.51
## 3    3b       NA
## 4    3c 83500.52
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      2.049414   0.216854   9.451   <2e-16 ***
## phi    -0.007112   0.004685  -1.518    0.129    
## alpha   0.780893   0.015254  51.193   <2e-16 ***
## A     131.000889   5.856863  22.367   <2e-16 ***
## k      32.455981   1.180812  27.486   <2e-16 ***
## p       0.186722   0.009448  19.763   <2e-16 ***
## s       2.290107   0.127126  18.014   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5425 on 7638 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.348e-06
##   (145 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   7771     2669.8                              
## 2   7770     2669.8   1   0.00   0.000      1    
## 3   7638     2247.0 132 422.83  10.889 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 83500.52
## 2     4 85766.57
## 3     5 85768.57
## 4     6 83497.02
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.903e+00  2.074e-01   9.177   <2e-16 ***
## phi   0.000e+00  4.679e-03   0.000        1    
## alpha 7.803e-01  1.524e-02  51.210   <2e-16 ***
## a     2.529e+01  9.630e-01  26.263   <2e-16 ***
## b     1.027e+02  5.028e+00  20.418   <2e-16 ***
## c     1.055e+02  7.798e+00  13.523   <2e-16 ***
## d     1.434e+00  6.274e-02  22.859   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5424 on 7638 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (145 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   7905     4072.2                                 
## 2   7904     4066.6   1   5.58  10.845 0.0009948 ***
## 3   7734     3731.9 170 334.69   4.080 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 88878.43
## 2     2 88869.59
## 3     3 86866.19
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    7.250e-01  1.821e-01   3.981 6.91e-05 ***
## phi   1.443e-02  5.585e-03   2.584  0.00978 ** 
## alpha 6.107e-01  2.691e-02  22.695  < 2e-16 ***
## A     2.312e+02  1.127e+01  20.522  < 2e-16 ***
## k     5.172e+01  2.622e+00  19.725  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6946 on 7734 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.112e-06
##   (201 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7734     3731.9                                 
## 2   7733     3561.2  1 170.777  370.84 < 2.2e-16 ***
## 3   7732     3486.0  1  75.186  166.77 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 86866.19
## 2    3a 86505.68
## 3    3b       NA
## 4    3c 86342.54
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.180e+00  2.037e-01   5.796 7.06e-09 ***
## phi   1.951e-02  5.268e-03   3.704 0.000214 ***
## alpha 8.157e-01  1.491e-02  54.709  < 2e-16 ***
## A     1.435e+02  7.160e+00  20.040  < 2e-16 ***
## k     3.445e+01  1.453e+00  23.704  < 2e-16 ***
## p     2.051e-01  1.124e-02  18.249  < 2e-16 ***
## s     2.380e+00  1.583e-01  15.031  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6715 on 7732 degrees of freedom
## 
## Number of iterations to convergence: 30 
## Achieved convergence tolerance: 8.441e-06
##   (201 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   7903     4029.5                                 
## 2   7902     4023.0   1   6.53 12.8240 0.0003443 ***
## 3   7732     3483.8 170 539.18  7.0391 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 86342.54
## 2     4 88799.14
## 3     5 88788.32
## 4     6 86337.79
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.150e+00  2.016e-01   5.703 1.22e-08 ***
## phi   1.931e-02  5.265e-03   3.668 0.000246 ***
## alpha 8.152e-01  1.490e-02  54.722  < 2e-16 ***
## a     2.973e+01  1.259e+00  23.612  < 2e-16 ***
## b     1.110e+02  6.334e+00  17.530  < 2e-16 ***
## c     1.133e+02  1.013e+01  11.182  < 2e-16 ***
## d     1.416e+00  7.419e-02  19.085  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6712 on 7732 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (201 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1    826     218.04                              
## 2    825     217.18  1  0.858  3.2587 0.07141 .  
## 3    796     176.62 29 40.558  6.3031 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9094.121
## 2     2 9092.853
## 3     3 8721.076
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.03331    0.42869  -0.078 0.938079    
## phi     0.02377    0.01704   1.395 0.163503    
## alpha   0.78853    0.06572  11.998  < 2e-16 ***
## A     773.16127  194.86026   3.968 7.91e-05 ***
## k     245.90341   70.09441   3.508 0.000477 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.471 on 796 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.03e-06
##   (29 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    796     176.62                           
## 2    795     176.57  1 0.053697  0.2418 0.6231
##   model      AIC
## 1     3 8721.076
## 2    3a 8722.832
## 3    3b 8722.697
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.03331    0.42869  -0.078 0.938079    
## phi     0.02377    0.01704   1.395 0.163503    
## alpha   0.78853    0.06572  11.998  < 2e-16 ***
## A     773.16127  194.86026   3.968 7.91e-05 ***
## k     245.90341   70.09441   3.508 0.000477 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.471 on 796 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.03e-06
##   (29 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Error in nls(f_5, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    824     216.69                                
## 2    794     176.36 30 40.328  6.0523 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8721.076
## 2     4 9092.966
## 3     5       NA
## 4     6 8723.879
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.03331    0.42869  -0.078 0.938079    
## phi     0.02377    0.01704   1.395 0.163503    
## alpha   0.78853    0.06572  11.998  < 2e-16 ***
## A     773.16127  194.86026   3.968 7.91e-05 ***
## k     245.90341   70.09441   3.508 0.000477 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.471 on 796 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.03e-06
##   (29 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9564, p-value = 1.117e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -10.183, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   1387     347.56                                  
## 2   1386     347.55   1   0.009  0.0358      0.85    
## 3    976     201.22 410 146.336  1.7312 4.576e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14526.30
## 2     2 14528.27
## 3     3 10148.74
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.72569    0.45999   1.578    0.115    
## phi    -0.01189    0.01093  -1.087    0.277    
## alpha   0.74240    0.08614   8.618  < 2e-16 ***
## A     233.44634   31.56045   7.397  3.0e-13 ***
## k      97.74632   14.64004   6.677  4.1e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4541 on 976 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.34e-06
##   (411 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    976     201.22                              
## 2    975     199.45  1 1.7642  8.6238 0.003396 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 10148.74
## 2    3a 10142.10
## 3    3b 10132.44
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.675553   0.446554   1.513    0.131    
## phi    -0.009984   0.010881  -0.917    0.359    
## alpha   0.758099   0.086092   8.806  < 2e-16 ***
## A     131.142574  15.123500   8.671  < 2e-16 ***
## k      36.877878   3.369293  10.945  < 2e-16 ***
## s       1.907117   0.235354   8.103 1.59e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4501 on 975 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.167e-06
##   (411 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   1385     337.23                                  
## 2   1384     337.21   1   0.028  0.1133    0.7364    
## 3    974     196.75 410 140.452  1.6958 2.805e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 10132.44
## 2     4 14488.37
## 3     5 14490.26
## 4     6 10130.73
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.52834    0.42228   1.251  0.21117    
## phi     0.00000    0.01109   0.000  1.00000    
## alpha   0.75256    0.08644   8.706  < 2e-16 ***
## a      20.68200    7.89781   2.619  0.00896 ** 
## b      94.56775   12.14165   7.789 1.73e-14 ***
## c     104.72342   10.87647   9.628  < 2e-16 ***
## d       1.19567    0.16622   7.193 1.26e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4495 on 974 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (411 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97083, p-value = 3.951e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.8579, p-value = 3.907e-15
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    439     237.09                                
## 2    438     236.77  1  0.320  0.5915    0.4423    
## 3    414     203.61 24 33.163  2.8095 1.648e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4609.958
## 2     2 4611.362
## 3     3 4398.952
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.06044    0.57866  -0.104    0.917    
## phi    -0.01117    0.02199  -0.508    0.612    
## alpha   0.52728    0.13377   3.942 9.49e-05 ***
## A     168.90330   33.06689   5.108 4.98e-07 ***
## k      48.88934   11.19265   4.368 1.59e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7013 on 414 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.307e-06
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_255,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    414     203.61                                
## 2    413     195.02  1 8.5942  18.201 2.468e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4398.952
## 2    3a 4382.882
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.20658    0.63441   0.326   0.7449    
## phi    -0.01148    0.02110  -0.544   0.5866    
## alpha   0.65556    0.09706   6.754 4.89e-11 ***
## A     350.53518  253.12950   1.385   0.1669    
## k     210.79807  205.12582   1.028   0.3047    
## p       0.04281    0.02445   1.751   0.0806 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6872 on 413 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 8.782e-06
##   (25 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    437     226.64                                
## 2    436     226.38  1  0.257   0.495    0.4821    
## 3    412     182.67 24 43.713   4.108 1.104e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 4382.882
## 2     4 4594.028
## 3     5 4595.526
## 4     6 4357.477
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.12210    0.58498   0.209    0.835    
## phi    0.00000    0.02007   0.000    1.000    
## alpha  0.72207    0.08300   8.700  < 2e-16 ***
## a     24.95845    3.47809   7.176 3.37e-12 ***
## b     67.55150    9.97122   6.775 4.32e-11 ***
## c     54.80781    4.97573  11.015  < 2e-16 ***
## d      0.85562    0.11805   7.248 2.10e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6659 on 412 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94119, p-value = 7.977e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.1487, p-value = 3.344e-05
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    149     87.775                         
## 2    148     87.770  1 0.0054  0.0091 0.9243
## 3    134     78.060 14 9.7102  1.1906 0.2895
##   model      AIC
## 1     1 1640.707
## 2     2 1642.698
## 3     3 1513.662
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.26596    2.70800   0.467 0.640911    
## phi     0.02123    0.04175   0.509 0.611881    
## alpha   1.02394    0.28761   3.560 0.000513 ***
## A     172.21708  111.72522   1.541 0.125569    
## k      97.50664   66.42911   1.468 0.144494    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7632 on 134 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.907e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 1513.662
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.26596    2.70800   0.467 0.640911    
## phi     0.02123    0.04175   0.509 0.611881    
## alpha   1.02394    0.28761   3.560 0.000513 ***
## A     172.21708  111.72522   1.541 0.125569    
## k      97.50664   66.42911   1.468 0.144494    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7632 on 134 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.907e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    147     83.369                         
## 2    146     83.369  1  0.000  0.0000 1.0000
## 3    132     72.682 14 10.688  1.3864 0.1682
##   model      AIC
## 1     3 1513.662
## 2     4 1636.879
## 3     5 1638.879
## 4     6 1507.740
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.229e+00  3.519e+00   0.634 0.527422    
## phi   4.601e-03  3.909e-02   0.118 0.906483    
## alpha 1.034e+00  2.781e-01   3.718 0.000296 ***
## a     2.383e+01  1.470e+01   1.621 0.107315    
## b     5.124e+01  3.508e+01   1.461 0.146476    
## c     1.160e+02  9.460e+01   1.227 0.222165    
## d     1.069e+00  7.322e-01   1.461 0.146518    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.742 on 132 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87905, p-value = 2.876e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.5188, p-value = 0.0004335
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5103     963.25                                 
## 2   5102     953.15  1  10.106  54.096 2.213e-13 ***
## 3   5087     816.07 15 137.075  56.964 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 54262.24
## 2     2 54210.39
## 3     3 53319.17
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.45428    0.15363   2.957  0.00312 ** 
## phi     0.02721    0.00411   6.620 3.95e-11 ***
## alpha   0.80377    0.02644  30.401  < 2e-16 ***
## A     412.15962   25.00388  16.484  < 2e-16 ***
## k     176.59637   11.52461  15.323  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4005 on 5087 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.867e-06
##   (16 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5087     816.07                                
## 2   5086     812.13  1 3.9424  24.689 6.957e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 53319.17
## 2    3a 53296.51
## 3    3b 53279.84
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    3.801e-01  1.484e-01   2.561   0.0105 *  
## phi   2.507e-02  4.077e-03   6.148 8.42e-10 ***
## alpha 8.123e-01  2.661e-02  30.529  < 2e-16 ***
## A     2.419e+02  1.643e+01  14.722  < 2e-16 ***
## k     6.902e+01  6.668e+00  10.352  < 2e-16 ***
## s     1.320e+00  5.481e-02  24.079  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3989 on 5086 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.448e-06
##   (16 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5101     952.58                                 
## 2   5100     943.77  1   8.811  47.612 5.829e-12 ***
## 3   5085     806.69 15 137.078  57.605 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 53279.84
## 2     4 54209.36
## 3     5 54163.91
## 4     6 53264.31
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.171e-01  1.510e-01   2.763  0.00575 ** 
## phi   2.471e-02  4.066e-03   6.078 1.31e-09 ***
## alpha 8.146e-01  2.613e-02  31.172  < 2e-16 ***
## a     1.948e+01  2.829e+00   6.886 6.45e-12 ***
## b     1.479e+02  9.524e+00  15.526  < 2e-16 ***
## c     1.749e+02  1.851e+01   9.447  < 2e-16 ***
## d     1.523e+00  1.005e-01  15.155  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3983 on 5085 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (16 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5180     879.40                                
## 2   5179     872.62  1  6.779  40.231 2.448e-10 ***
## 3   5151     806.45 28 66.178  15.096 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 57351.18
## 2     2 57313.08
## 3     3 56678.87
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.063850   0.161829   6.574 5.39e-11 ***
## phi    -0.030024   0.004525  -6.635 3.58e-11 ***
## alpha   0.828797   0.041483  19.979  < 2e-16 ***
## A     244.905969   9.585367  25.550  < 2e-16 ***
## k      57.563428   2.889563  19.921  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3957 on 5151 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.999e-06
##   (30 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   5151     806.45                               
## 2   5150     806.45  1  0.0005   0.0034 0.9535    
## 3   5150     802.47  0  0.0000                    
## 4   5149     783.02  1 19.4478 127.8852 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 56678.87
## 2    3a 56680.87
## 3    3b 56655.37
## 4    3c 56530.88
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.26879    0.17208   7.373 1.93e-13 ***
## phi    -0.03036    0.00444  -6.838 8.96e-12 ***
## alpha   0.83333    0.03778  22.056  < 2e-16 ***
## A     150.83652    5.37184  28.079  < 2e-16 ***
## k      38.54357    1.02378  37.648  < 2e-16 ***
## p       0.26168    0.01751  14.944  < 2e-16 ***
## s       3.02312    0.23227  13.016  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.39 on 5149 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.986e-06
##   (30 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   5178     862.65                             
## 2   5177     862.65  1  0.000   0.000      1    
## 3   5149     789.00 28 73.645  17.164 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 56530.88
## 2     4 57255.49
## 3     5 57257.49
## 4     6 56570.14
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.26879    0.17208   7.373 1.93e-13 ***
## phi    -0.03036    0.00444  -6.838 8.96e-12 ***
## alpha   0.83333    0.03778  22.056  < 2e-16 ***
## A     150.83652    5.37184  28.079  < 2e-16 ***
## k      38.54357    1.02378  37.648  < 2e-16 ***
## p       0.26168    0.01751  14.944  < 2e-16 ***
## s       3.02312    0.23227  13.016  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.39 on 5149 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.986e-06
##   (30 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    596     80.866                                
## 2    595     78.165  1 2.7013  20.563 6.981e-06 ***
## 3    593     69.832  2 8.3328  35.381 3.049e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6115.535
## 2     2 6097.184
## 3     3 6024.464
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.65199    0.22705  -2.872 0.004231 ** 
## phi     0.06644    0.01727   3.847 0.000133 ***
## alpha   0.87209    0.09746   8.948  < 2e-16 ***
## A     328.23839   44.23555   7.420 4.07e-13 ***
## k      95.23106   18.35173   5.189 2.90e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3432 on 593 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.679e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    593     69.832                           
## 2    592     69.732  1 0.099537   0.845 0.3583
##   model      AIC
## 1     3 6024.464
## 2    3a 6025.611
## 3    3b 6026.057
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.65199    0.22705  -2.872 0.004231 ** 
## phi     0.06644    0.01727   3.847 0.000133 ***
## alpha   0.87209    0.09746   8.948  < 2e-16 ***
## A     328.23839   44.23555   7.420 4.07e-13 ***
## k      95.23106   18.35173   5.189 2.90e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3432 on 593 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.679e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    594     80.723                                
## 2    593     78.002  1 2.7205  20.682 6.577e-06 ***
## 3    591     69.748  2 8.2546  34.972 4.419e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6024.464
## 2     4 6118.473
## 3     5 6099.938
## 4     6 6027.743
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.65199    0.22705  -2.872 0.004231 ** 
## phi     0.06644    0.01727   3.847 0.000133 ***
## alpha   0.87209    0.09746   8.948  < 2e-16 ***
## A     328.23839   44.23555   7.420 4.07e-13 ***
## k      95.23106   18.35173   5.189 2.90e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3432 on 593 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.679e-06
##   (4 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96799, p-value = 3.877e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.2615, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    676     152.77                                 
## 2    675     152.74  1  0.0331  0.1463    0.7022    
## 3    668     137.45  7 15.2872 10.6137 1.062e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7025.553
## 2     2 7027.406
## 3     3 6914.896
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.88582    0.65606   1.350    0.177    
## phi    -0.01472    0.01648  -0.893    0.372    
## alpha   0.88301    0.11088   7.964 7.21e-15 ***
## A     271.33123   53.95943   5.028 6.36e-07 ***
## k     127.77529   26.81374   4.765 2.32e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4536 on 668 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.662e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    668     137.45                          
## 2    667     137.06  1 0.38606  1.8787 0.1709
##   model      AIC
## 1     3 6914.896
## 2    3a 6915.003
## 3    3b 6915.692
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.88582    0.65606   1.350    0.177    
## phi    -0.01472    0.01648  -0.893    0.372    
## alpha   0.88301    0.11088   7.964 7.21e-15 ***
## A     271.33123   53.95943   5.028 6.36e-07 ***
## k     127.77529   26.81374   4.765 2.32e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4536 on 668 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.662e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    674     152.71                                 
## 2    673     152.68  1  0.0292  0.1285    0.7201    
## 3    666     136.87  7 15.8066 10.9877 3.553e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6914.896
## 2     4 7029.273
## 3     5 7031.144
## 4     6 6916.058
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.88582    0.65606   1.350    0.177    
## phi    -0.01472    0.01648  -0.893    0.372    
## alpha   0.88301    0.11088   7.964 7.21e-15 ***
## A     271.33123   53.95943   5.028 6.36e-07 ***
## k     127.77529   26.81374   4.765 2.32e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4536 on 668 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.662e-06
##   (7 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96139, p-value = 2.614e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.552, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    326    100.337                          
## 2    325    100.079   1  0.258  0.8374 0.3608
## 3    158     52.814 167 47.265  0.8467 0.8555
##   model      AIC
## 1     1 3504.259
## 2     2 3505.412
## 3     3 1759.456
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge     -1.48606    1.41220  -1.052   0.2943   
## phi     0.01272    0.04987   0.255   0.7990   
## alpha   0.76925    0.26956   2.854   0.0049 **
## A     203.25021  140.15841   1.450   0.1490   
## k      14.85544   10.51749   1.412   0.1598   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5782 on 158 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 6.912e-06
##   (167 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    158     52.814                          
## 2    157     52.358  1 0.45656   1.369 0.2438
##   model      AIC
## 1     3 1759.456
## 2    3a 1760.041
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge     -1.48606    1.41220  -1.052   0.2943   
## phi     0.01272    0.04987   0.255   0.7990   
## alpha   0.76925    0.26956   2.854   0.0049 **
## A     203.25021  140.15841   1.450   0.1490   
## k      14.85544   10.51749   1.412   0.1598   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5782 on 158 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 6.912e-06
##   (167 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    324     96.856                          
## 2    323     96.193   1  0.664  2.2281 0.1365
## 3    156     50.242 167 45.951  0.8543 0.8414
##   model      AIC
## 1     3 1759.456
## 2     4 3496.641
## 3     5 3496.380
## 4     6 1755.317
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.51727    1.33141  -1.140   0.2562    
## phi     0.02239    0.04716   0.475   0.6356    
## alpha   0.65620    0.29602   2.217   0.0281 *  
## a       0.00000  140.98559   0.000   1.0000    
## b     195.96813  183.67096   1.067   0.2876    
## c     113.88013   16.52715   6.890 1.29e-10 ***
## d       1.69907    0.94346   1.801   0.0737 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5675 on 156 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (167 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98286, p-value = 0.04139
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.2756, p-value = 0.7829
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    299    124.348                         
## 2    298    124.343  1  0.005  0.0123 0.9116
## 3    212     86.586 86 37.757  1.0750 0.3349
##   model      AIC
## 1     1 3013.807
## 2     2 3015.794
## 3     3 2168.484
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.662886   1.134146  -0.584  0.55952    
## phi     0.003057   0.035527   0.086  0.93151    
## alpha   0.787867   0.134017   5.879 1.59e-08 ***
## A     119.692211  43.815875   2.732  0.00683 ** 
## k      51.043598  22.851590   2.234  0.02655 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6391 on 212 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.69e-06
##   (89 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    212     86.586                          
## 2    211     86.584  1 0.00194  0.0047 0.9452
## 3    211     86.462  0 0.00000               
## 4    210     86.173  1 0.28851  0.7031 0.4027
##   model      AIC
## 1     3 2168.484
## 2    3a 2170.479
## 3    3b 2170.172
## 4    3c 2171.446
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.662886   1.134146  -0.584  0.55952    
## phi     0.003057   0.035527   0.086  0.93151    
## alpha   0.787867   0.134017   5.879 1.59e-08 ***
## A     119.692211  43.815875   2.732  0.00683 ** 
## k      51.043598  22.851590   2.234  0.02655 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6391 on 212 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.69e-06
##   (89 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    297     124.07                         
## 2    296     124.07  1  0.000  0.0000 1.0000
## 3    210      86.54 86 37.528  1.0589 0.3661
##   model      AIC
## 1     3 2168.484
## 2     4 3017.126
## 3     5 3019.126
## 4     6 2172.369
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.662886   1.134146  -0.584  0.55952    
## phi     0.003057   0.035527   0.086  0.93151    
## alpha   0.787867   0.134017   5.879 1.59e-08 ***
## A     119.692211  43.815875   2.732  0.00683 ** 
## k      51.043598  22.851590   2.234  0.02655 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6391 on 212 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.69e-06
##   (89 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92281, p-value = 3.121e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.6099, p-value = 0.009057
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 3 6 6
212 Laurentian Mixed Forest 3c 6 6
221 Eastern Broadleaf Forest 3b 6 6
222 Midwest Broadleaf Forest 3 6 6
223 Central Interior Broadleaf Forest 3b 6 6
231 Southeastern Mixed Forest 3c 6 6
232 Outer Coastal Plain Mixed Forest 3c 6 6
234 Lower Mississippi Riverine Forest 3 3 3
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 3b 6 6
255 Prairie Parkland (Subtropical) 3a 6 6
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA NA NA
313 Colorado Plateau Semi-Desert NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe NA NA NA
332 Great Plains Steppe 3 6 6
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3b 6 6
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3c 3c 3c
M223 Ozark Broadleaf Forest Meadow 3 3 3
M231 Ouachita Mixed Forest 3 3 3
M242 Cascade Mixed Forest NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3 6 6
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M334 Black Hills Coniferous Forest 3 3 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA NA NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.se b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.2877780 0.0287453 -0.0446067 0.6201626 0.0213071 0.0000258 0.0113529 0.0312613 0.8506776 0.0010705 0.7865357 0.9148196 471.9581 403.50112 540.4152 191.34583 159.314916 223.37675 41.87458 37.982973 45.76619 114.43920 NA 104.05677 124.82163 111.99553 103.23997 120.7511 0.8929408 0.8078949 0.9779866
212 Laurentian Mixed Forest east 12962 6481 0.2375598 0.0204719 -0.0429069 0.5180266 0.0157806 0.0000164 0.0078382 0.0237231 0.7919628 0.0003927 0.7531169 0.8308086 123.9152 113.44105 134.3894 46.47178 43.311348 49.63222 24.94954 23.015693 26.88340 86.17965 NA 79.62083 92.73847 119.30997 108.73249 129.8875 1.2504323 1.1613832 1.3394814
221 Eastern Broadleaf Forest east 5446 2723 0.2335590 0.0181260 -0.0303756 0.4974937 0.0000000 0.0000161 -0.0078628 0.0078628 0.8140497 0.0008966 0.7553476 0.8727517 317.0920 263.17442 371.0096 72.66406 54.460022 90.86810 29.92583 24.527782 35.32388 166.53295 NA 148.56212 184.50377 142.75973 118.81337 166.7061 1.3752196 1.2168728 1.5335664
222 Midwest Broadleaf Forest east 3552 1776 -0.3913884 0.0458539 -0.8112717 0.0284948 0.0440710 0.0001297 0.0217421 0.0664000 0.8455980 0.0022501 0.7525864 0.9386096 510.0740 393.89458 626.2535 204.81027 152.111703 257.50884 28.12536 23.763183 32.48753 125.18955 NA 110.25587 140.12323 104.14395 92.34256 115.9453 1.0133386 0.8930635 1.1336136
223 Central Interior Broadleaf Forest east 6388 3194 -0.1998960 0.0133494 -0.4264016 0.0266096 0.0000000 0.0000320 -0.0110950 0.0110950 0.7613860 0.0010859 0.6967844 0.8259876 192.9556 171.30911 214.6021 40.23543 34.041793 46.42907 31.44045 25.722935 37.15796 117.40902 NA 107.20911 127.60894 106.43496 94.52851 118.3414 1.2637100 1.1181751 1.4092448
231 Southeastern Mixed Forest east 7790 3895 1.9030316 0.0430033 1.4965246 2.3095385 0.0000000 0.0000219 -0.0091714 0.0091714 0.7803165 0.0002322 0.7504464 0.8101865 131.0009 119.51983 142.4819 32.45598 30.141264 34.77070 25.28970 23.402041 27.17736 102.66171 NA 92.80545 112.51797 105.45703 90.17028 120.7438 1.4341063 1.3111268 1.5570858
232 Outer Coastal Plain Mixed Forest east 7940 3970 1.1500067 0.0406599 0.7547318 1.5452815 0.0193128 0.0000277 0.0089922 0.0296334 0.8152161 0.0002219 0.7860133 0.8444188 143.4801 129.44490 157.5153 34.45142 31.602370 37.30047 29.73291 27.264532 32.20130 111.04165 NA 98.62444 123.45887 113.30665 93.44343 133.1699 1.4158887 1.2704611 1.5613163
234 Lower Mississippi Riverine Forest east 830 415 -0.0333131 0.1837739 -0.8748068 0.8081806 0.0237660 0.0002904 -0.0096837 0.0572157 0.7885292 0.0043191 0.6595244 0.9175340 773.1613 390.66059 1155.6620 245.90341 108.311676 383.49515 NA NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.5283403 0.1783177 -0.3003368 1.3570175 0.0000000 0.0001229 -0.0217547 0.0217547 0.7525580 0.0074718 0.5829283 0.9221876 131.1426 101.46422 160.8209 36.87788 30.265978 43.48978 20.68200 5.183318 36.18069 94.56775 NA 70.74096 118.39455 104.72342 83.37941 126.0674 1.1956744 0.8694895 1.5218593
255 Prairie Parkland (Subtropical) east 444 222 0.1221031 0.3422036 -1.0278180 1.2720243 0.0000000 0.0004029 -0.0394581 0.0394581 0.7220666 0.0068888 0.5589130 0.8852202 350.5352 -147.04769 848.1180 210.79807 -192.422792 614.01894 24.95845 18.121437 31.79546 67.55150 NA 47.95070 87.15231 54.80781 45.02682 64.5888 0.8556175 0.6235703 1.0876647
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 2.2294804 12.3806175 -4.7306783 9.1896391 0.0046009 0.0015280 -0.0727225 0.0819244 1.0341635 0.0773616 0.4839760 1.5843511 172.2171 -48.75594 393.1901 97.50664 -33.878566 228.89185 23.83275 -5.242830 52.90833 51.23735 NA -18.14923 120.62392 116.03061 -71.09191 303.1531 1.0694239 -0.3789640 2.5178118
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 0.4171085 0.0227937 0.1211312 0.7130858 0.0247145 0.0000165 0.0167425 0.0326865 0.8146370 0.0006829 0.7634045 0.8658695 241.8804 209.67019 274.0905 69.02288 55.950986 82.09478 19.48247 13.935512 25.02943 147.87253 NA 129.20045 166.54461 174.87696 138.58584 211.1681 1.5230639 1.3260432 1.7200846
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 1.2687929 0.0296116 0.9314425 1.6061433 -0.0303623 0.0000197 -0.0390669 -0.0216577 0.8333259 0.0014275 0.7592578 0.9073941 150.8365 140.30543 161.3676 38.54357 36.536536 40.55061 NA NA NA NA NA NA NA NA NA NA NA NA NA
M223 Ozark Broadleaf Forest Meadow east 602 301 -0.6519872 0.0515526 -1.0979110 -0.2060634 0.0664387 0.0002983 0.0325206 0.1003568 0.8720875 0.0094986 0.6806772 1.0634977 328.2384 241.36099 415.1158 95.23106 59.188766 131.27336 NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 680 340 0.8858234 0.4304136 -0.4023629 2.1740096 -0.0147199 0.0002715 -0.0470704 0.0176306 0.8830080 0.0122945 0.6652915 1.1007244 271.3312 165.38073 377.2817 127.77529 75.125933 180.42465 NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 330 165 -1.5172712 1.7726606 -4.1471947 1.1126523 0.0223906 0.0022241 -0.0707641 0.1155453 0.6562001 0.0876307 0.0714661 1.2409341 203.2502 -73.57555 480.0760 14.85544 -5.917571 35.62846 0.00000 -278.487071 278.48707 195.96813 NA -166.83483 558.77109 113.88013 81.23426 146.5260 1.6990664 -0.1645364 3.5626693
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 306 153 -0.6628862 1.2862864 -2.8985335 1.5727610 0.0030572 0.0012622 -0.0669749 0.0730893 0.7878674 0.0179606 0.5236907 1.0520442 119.6922 33.32161 206.0628 51.04360 5.998156 96.08904 NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot phi (effect of DeltaPDSI)

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 19 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 19 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region  weighted.ge weighted.ge.std_Error 95 % CI, upper
## 1     entire US  0.566036010           0.057633715    0.678998091
## 2       pacific -0.007795900           0.006840941    0.005612345
## 3          east  0.571644372           0.056342414    0.682075503
## 4 interior west  0.002187538           0.010018934    0.021824648
##   95 % CI, lower
## 1     0.45307393
## 2    -0.02120415
## 3     0.46121324
## 4    -0.01744957

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US 1.004334e-02           0.0017032896   0.0133817874
## 2       pacific 1.150454e-04           0.0002423134   0.0005899797
## 3          east 9.902697e-03           0.0016748263   0.0131853562
## 4 interior west 2.559775e-05           0.0001934853   0.0004048289
##   95 % CI, lower
## 1   0.0067048921
## 2  -0.0003598890
## 3   0.0066200371
## 4  -0.0003536334

alpha (biomass compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.801557954             0.0087472586    0.818702581
## 2       pacific    0.003371626             0.0015210066    0.006352799
## 3          east    0.791952893             0.0085643792    0.808739076
## 4 interior west    0.006233435             0.0009232988    0.008043101
##   95 % CI, lower
## 1   0.7844133275
## 2   0.0003904528
## 3   0.7751667100
## 4   0.0044237698

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   223.1264
## 2       pacific   182.2624
## 3          east   224.6030
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   70.31344
## 2       pacific   13.32146
## 3          east   70.86571
## 4 interior west   48.32076

Model Bookeeping

1. Delta-B due to Delta-STDAGE

2. Delta-B due to Delta-Year (ge)

make a fig

## Warning: Removed 12504 rows containing missing values (geom_point).

3. stand age densities

make a fig

## Warning: package 'ggridges' was built under R version 4.2.2
## Picking joint bandwidth of 7.36


Analysis 2: Temporally-balanced, No-harvest

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3758     873.45                                
## 2   3757     871.73  1  1.722  7.4221  0.006473 ** 
## 3   3725     801.01 32 70.721 10.2776 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40904.91
## 2     2 40899.49
## 3     3 40329.41
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.44857    0.20583   2.179  0.02937 *  
## phi     0.01735    0.00574   3.023  0.00252 ** 
## alpha   1.18650    0.06958  17.052  < 2e-16 ***
## A     449.33176   38.06338  11.805  < 2e-16 ***
## k     191.61411   18.22818  10.512  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4637 on 3725 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.391e-06
##   (32 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1   3725     801.01                             
## 2   3724     801.01  1 0.00012996   6e-04 0.9804
##   model      AIC
## 1     3 40329.41
## 2    3a 40331.41
## 3    3b 40326.08
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.297e-01  2.039e-01   2.107  0.03515 *  
## phi   1.696e-02  5.747e-03   2.951  0.00319 ** 
## alpha 1.191e+00  7.011e-02  16.994  < 2e-16 ***
## A     3.140e+02  4.544e+01   6.910 5.69e-12 ***
## k     1.031e+02  2.332e+01   4.422 1.01e-05 ***
## s     1.165e+00  7.803e-02  14.924  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4634 on 3724 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.238e-06
##   (32 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3756     857.29                                
## 2   3755     855.77  1  1.514  6.6444  0.009985 ** 
## 3   3723     781.01 32 74.766 11.1376 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 40326.08
## 2     4 40838.67
## 3     5 40834.02
## 4     6 40239.10
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    6.302e-01  2.188e-01   2.880  0.00400 ** 
## phi   1.693e-02  5.673e-03   2.985  0.00286 ** 
## alpha 1.170e+00  6.853e-02  17.070  < 2e-16 ***
## a     3.894e+01  2.230e+00  17.459  < 2e-16 ***
## b     1.122e+02  6.313e+00  17.780  < 2e-16 ***
## c     1.162e+02  5.721e+00  20.307  < 2e-16 ***
## d     9.315e-01  5.285e-02  17.626  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.458 on 3723 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (32 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98702, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -25.889, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df  Sum Sq F value    Pr(>F)    
## 1  10460     3892.5                                   
## 2  10457     3882.9    3    9.59  8.6080 1.054e-05 ***
## 3   7874     2744.9 2583 1137.99  1.2638 4.800e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 109465.57
## 2     2 109421.55
## 3     3  82461.78
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    6.899e-02  1.466e-01   0.471    0.638    
## phi   2.316e-02  4.553e-03   5.088 3.71e-07 ***
## alpha 9.137e-01  4.640e-02  19.693  < 2e-16 ***
## A     1.839e+02  8.007e+00  22.968  < 2e-16 ***
## k     6.688e+01  3.214e+00  20.812  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5904 on 7874 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.225e-06
##   (2591 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7874     2744.9                                
## 2   7873     2740.5  1  4.459  12.809  0.000347 ***
## 3   7873     2744.9  0  0.000                      
## 4   7872     2710.2  1 34.680 100.731 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 82461.78
## 2    3a 82450.98
## 3    3b 82463.74
## 4    3c 82365.56
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.511e-01  1.515e-01   0.997    0.319    
## phi   2.196e-02  4.511e-03   4.869 1.14e-06 ***
## alpha 9.058e-01  4.340e-02  20.871  < 2e-16 ***
## A     1.249e+02  6.258e+00  19.957  < 2e-16 ***
## k     4.582e+01  1.993e+00  22.988  < 2e-16 ***
## p     1.788e-01  1.531e-02  11.680  < 2e-16 ***
## s     2.094e+00  1.541e-01  13.585  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5868 on 7872 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 7.906e-06
##   (2591 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df  Sum Sq F value    Pr(>F)    
## 1  10458     3839.4                                   
## 2  10455     3831.6    3    7.76  7.0593 9.764e-05 ***
## 3   7872     2703.3 2583 1128.38  1.2721 9.390e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1    3c  82365.56
## 2     4 109325.84
## 3     5 109286.47
## 4     6  82345.24
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.809e-01  1.532e-01   1.180    0.238    
## phi   2.119e-02  4.501e-03   4.709 2.53e-06 ***
## alpha 9.083e-01  4.320e-02  21.026  < 2e-16 ***
## a     2.358e+01  1.308e+00  18.029  < 2e-16 ***
## b     8.645e+01  3.883e+00  22.261  < 2e-16 ***
## c     1.254e+02  7.218e+00  17.369  < 2e-16 ***
## d     1.351e+00  6.256e-02  21.593  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.586 on 7872 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2591 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   4456     722.50                             
## 2   4455     722.49  1  0.002  0.0154 0.9013    
## 3   4421     670.60 34 51.899 10.0633 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 48766.23
## 2     2 48768.22
## 3     3 48166.70
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     5.303e-01  1.674e-01   3.169  0.00154 ** 
## phi   -9.616e-04  4.453e-03  -0.216  0.82905    
## alpha  9.230e-01  5.191e-02  17.782  < 2e-16 ***
## A      4.435e+02  2.951e+01  15.031  < 2e-16 ***
## k      1.434e+02  1.095e+01  13.096  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3895 on 4421 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.44e-06
##   (34 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   4421     670.60                              
## 2   4420     669.49  1 1.1033  7.2841 0.006983 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 48166.70
## 2    3a 48161.41
## 3    3b 48144.77
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.593464   0.171933   3.452 0.000562 ***
## phi    -0.001691   0.004437  -0.381 0.703039    
## alpha   0.932788   0.052390  17.805  < 2e-16 ***
## A     269.299929  21.851620  12.324  < 2e-16 ***
## k      61.793839   6.743968   9.163  < 2e-16 ***
## s       1.336106   0.072380  18.459  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3885 on 4420 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.634e-06
##   (34 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   4454     713.75                             
## 2   4453     713.75  1  0.000   0.000      1    
## 3   4419     662.39 34 51.355  10.076 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 48144.77
## 2     4 48715.91
## 3     5 48717.91
## 4     6 48116.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    6.043e-01  1.720e-01   3.512 0.000449 ***
## phi   0.000e+00  4.436e-03   0.000 1.000000    
## alpha 9.248e-01  5.169e-02  17.891  < 2e-16 ***
## a     2.791e+01  3.095e+00   9.018  < 2e-16 ***
## b     1.518e+02  8.724e+00  17.399  < 2e-16 ***
## c     1.330e+02  1.063e+01  12.513  < 2e-16 ***
## d     1.318e+00  8.223e-02  16.029  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3872 on 4419 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (34 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98522, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -27.874, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   2793     944.73                                  
## 2   2792     941.04   1   3.698 10.9728 0.0009364 ***
## 3   2140     667.70 652 273.335  1.3436 7.999e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 30090.45
## 2     2 30081.49
## 3     3 23131.25
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.43802    0.24074  -1.820  0.06897 .  
## phi     0.04284    0.01303   3.287  0.00103 ** 
## alpha   0.94629    0.07841  12.069  < 2e-16 ***
## A     555.26223   80.49540   6.898 6.92e-12 ***
## k     234.54724   37.91141   6.187 7.34e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5586 on 2140 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.669e-06
##   (653 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   2140     667.70                              
## 2   2139     665.23  1 2.4744  7.9562 0.004837 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 23131.25
## 2    3a 23125.29
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.42210    0.24225  -1.742 0.081579 .  
## phi     0.04353    0.01303   3.341 0.000848 ***
## alpha   0.96338    0.07847  12.277  < 2e-16 ***
## A     415.29178   63.16060   6.575 6.09e-11 ***
## k     145.60494   32.08423   4.538 5.99e-06 ***
## p      -0.02285    0.01221  -1.871 0.061451 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5577 on 2139 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.52e-06
##   (653 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   2791     928.22                                  
## 2   2790     924.40   1   3.826 11.5480 0.0006877 ***
## 3   2138     650.78 652 273.614  1.3787 8.666e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 23125.29
## 2     4 30045.16
## 3     5 30035.61
## 4     6 23080.20
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.30194    0.25505  -1.184 0.236605    
## phi     0.04571    0.01297   3.523 0.000436 ***
## alpha   0.97764    0.07473  13.083  < 2e-16 ***
## a      25.34285    2.55168   9.932  < 2e-16 ***
## b     125.49277    8.96784  13.994  < 2e-16 ***
## c     105.73419    7.14126  14.806  < 2e-16 ***
## d       1.03559    0.07112  14.561  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5517 on 2138 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (653 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96192, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -15.636, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value   Pr(>F)    
## 1   5108     929.31                                
## 2   5107     926.24   1   3.07 16.9250 3.95e-05 ***
## 3   4257     767.63 850 158.62  1.0349   0.2549    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 53477.85
## 2     2 53462.94
## 3     3 44740.59
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.037514   0.143266   0.262  0.79345    
## phi    -0.017291   0.006144  -2.814  0.00491 ** 
## alpha   0.849970   0.056531  15.036  < 2e-16 ***
## A     290.320466  15.959640  18.191  < 2e-16 ***
## k      87.121972   6.114438  14.249  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4246 on 4257 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.703e-06
##   (850 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   4257     767.63                          
## 2   4256     767.38  1 0.24491  1.3583 0.2439
##   model      AIC
## 1     3 44740.59
## 2    3a 44741.23
## 3    3b 44708.00
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.072750   0.145011   0.502  0.61591    
## phi    -0.017575   0.006106  -2.878  0.00402 ** 
## alpha   0.862833   0.056925  15.157  < 2e-16 ***
## A     187.602452  11.090419  16.916  < 2e-16 ***
## k      40.382048   3.004623  13.440  < 2e-16 ***
## s       1.484595   0.085160  17.433  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.423 on 4256 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 1.543e-06
##   (850 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)  
## 1   5106     913.48                             
## 2   5105     913.48   1   0.00  0.0000 0.99999  
## 3   4255     751.00 850 162.49  1.0831 0.06339 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 44708.00
## 2     4 53394.02
## 3     5 53396.02
## 4     6 44651.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.088713   0.134486   -0.66     0.51    
## phi     0.000000   0.006259    0.00     1.00    
## alpha   0.851800   0.055876   15.24   <2e-16 ***
## a      29.949354   2.877660   10.41   <2e-16 ***
## b     116.927942   5.395173   21.67   <2e-16 ***
## c     104.057685   5.723300   18.18   <2e-16 ***
## d       1.209447   0.071748   16.86   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4201 on 4255 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (850 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)    
## 1   6088     1450.4                               
## 2   6087     1450.3   1   0.128  0.5378 0.4634    
## 3   5968     1320.5 119 129.735  4.9270 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66409.03
## 2     2 66410.49
## 3     3 64983.46
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.525776   0.182829   8.345   <2e-16 ***
## phi    -0.002669   0.004681  -0.570    0.569    
## alpha   0.825622   0.047959  17.215   <2e-16 ***
## A     248.135533  10.671797  23.252   <2e-16 ***
## k      65.157321   2.827731  23.042   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4704 on 5968 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.173e-06
##   (119 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5968     1320.5                                 
## 2   5967     1319.8  1  0.7707  3.4845     0.062 .  
## 3   5967     1320.1  0  0.0000                      
## 4   5966     1308.2  1 11.9907 54.6854 1.609e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 64983.46
## 2    3a 64981.97
## 3    3b 64983.61
## 4    3c 64931.11
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.620931   0.188921   8.580  < 2e-16 ***
## phi    -0.002900   0.004649  -0.624    0.533    
## alpha   0.835793   0.046899  17.821  < 2e-16 ***
## A     159.443801   8.574543  18.595  < 2e-16 ***
## k      34.733065   1.937860  17.923  < 2e-16 ***
## p       0.098487   0.014242   6.915 5.16e-12 ***
## s       1.692332   0.115606  14.639  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4683 on 5966 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 4.557e-06
##   (119 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   6086     1437.5                              
## 2   6085     1437.5   1   0.00  0.0000      1    
## 3   5966     1307.1 119 130.34  4.9994 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 64931.11
## 2     4 66358.45
## 3     5 66360.45
## 4     6 64926.45
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.568e+00  1.857e-01   8.447   <2e-16 ***
## phi   0.000e+00  4.644e-03   0.000        1    
## alpha 8.342e-01  4.686e-02  17.801   <2e-16 ***
## a     1.689e+01  1.638e+00  10.310   <2e-16 ***
## b     1.280e+02  7.659e+00  16.707   <2e-16 ***
## c     1.380e+02  1.647e+01   8.376   <2e-16 ***
## d     1.788e+00  1.035e-01  17.274   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4681 on 5966 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (119 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   6290     2432.4                                  
## 2   6289     2429.8   1   2.678  6.9325  0.008485 ** 
## 3   6149     2238.4 140 191.372  3.7551 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70632.57
## 2     2 70627.64
## 3     3 69028.99
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    9.499e-01  1.980e-01   4.796 1.65e-06 ***
## phi   9.452e-03  5.430e-03   1.741   0.0818 .  
## alpha 7.839e-01  4.707e-02  16.653  < 2e-16 ***
## A     2.624e+02  1.416e+01  18.536  < 2e-16 ***
## k     6.860e+01  3.799e+00  18.056  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6033 on 6149 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.143e-06
##   (142 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6149     2238.4                                 
## 2   6148     2232.1  1  6.2484   17.21 3.392e-05 ***
## 3   6148     2238.2  0  0.0000                      
## 4   6147     2211.9  1 26.3325   73.18 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 69028.99
## 2    3a 69013.78
## 3    3b 69030.55
## 4    3c 68959.72
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.057e+00  2.048e-01   5.161 2.54e-07 ***
## phi   1.114e-02  5.375e-03   2.072   0.0383 *  
## alpha 8.077e-01  4.419e-02  18.279  < 2e-16 ***
## A     1.616e+02  9.596e+00  16.837  < 2e-16 ***
## k     3.606e+01  2.087e+00  17.281  < 2e-16 ***
## p     1.288e-01  1.577e-02   8.164 3.90e-16 ***
## s     1.880e+00  1.460e-01  12.879  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5999 on 6147 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 8.126e-06
##   (142 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)    
## 1   6288     2414.5                               
## 2   6287     2411.3   1   3.197  8.3359 0.0039 ** 
## 3   6147     2210.9 140 200.339  3.9785 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 68959.72
## 2     4 70589.95
## 3     5 70583.61
## 4     6 68957.08
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.040e+00  2.036e-01   5.106 3.39e-07 ***
## phi   1.097e-02  5.372e-03   2.042   0.0412 *  
## alpha 8.063e-01  4.417e-02  18.253  < 2e-16 ***
## a     2.148e+01  1.831e+00  11.732  < 2e-16 ***
## b     1.294e+02  8.811e+00  14.682  < 2e-16 ***
## c     1.367e+02  1.749e+01   7.818 6.26e-15 ***
## d     1.672e+00  1.093e-01  15.298  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5997 on 6147 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (142 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    675     158.75                                 
## 2    674     157.88  1  0.8713  3.7194    0.0542 .  
## 3    652     137.37 22 20.5192  4.4270 1.476e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7483.277
## 2     2 7481.546
## 3     3 7228.523
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05481    0.48055   0.114 0.909231    
## phi     0.02653    0.01807   1.468 0.142506    
## alpha   0.89149    0.10373   8.594  < 2e-16 ***
## A     622.17392  149.14819   4.172 3.44e-05 ***
## k     187.66098   51.26819   3.660 0.000272 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.459 on 652 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.757e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    652     137.37                           
## 2    651     137.32  1 0.049153   0.233 0.6294
##   model      AIC
## 1     3 7228.523
## 2    3a 7230.288
## 3    3b 7230.439
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05481    0.48055   0.114 0.909231    
## phi     0.02653    0.01807   1.468 0.142506    
## alpha   0.89149    0.10373   8.594  < 2e-16 ***
## A     622.17392  149.14819   4.172 3.44e-05 ***
## k     187.66098   51.26819   3.660 0.000272 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.459 on 652 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.757e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Error in nls(f_6, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df   Sum Sq F value  Pr(>F)  
## 1    673     158.11                                
## 2    672     157.27    1   0.8398  3.5885 0.05861 .
## 3    794     176.36 -122 -19.0827  0.6683 0.99681  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 7228.523
## 2     4 7484.532
## 3     5 7482.921
## 4     6 8723.879
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05481    0.48055   0.114 0.909231    
## phi     0.02653    0.01807   1.468 0.142506    
## alpha   0.89149    0.10373   8.594  < 2e-16 ***
## A     622.17392  149.14819   4.172 3.44e-05 ***
## k     187.66098   51.26819   3.660 0.000272 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.459 on 652 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.757e-06
##   (27 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96038, p-value = 2.573e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.4259, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   1213     319.61                                  
## 2   1212     319.58   1   0.028  0.1069    0.7438    
## 3    865     177.86 347 141.724  1.9864 8.171e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 12758.145
## 2     2 12760.038
## 3     3  9002.571
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.79489    0.50209   1.583    0.114    
## phi    -0.01295    0.01145  -1.131    0.258    
## alpha   0.76389    0.11156   6.847 1.43e-11 ***
## A     235.64874   34.70425   6.790 2.08e-11 ***
## k     100.50604   16.52225   6.083 1.77e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4534 on 865 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.737e-06
##   (348 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    865     177.86                          
## 2    864     177.47  1 0.38965   1.897 0.1688
##   model      AIC
## 1     3 9002.571
## 2    3a 9002.663
## 3    3b 8999.426
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.75249    0.49320   1.526    0.127    
## phi    -0.01115    0.01148  -0.971    0.332    
## alpha   0.77831    0.11201   6.949 7.26e-12 ***
## A     151.42691   24.69003   6.133 1.31e-09 ***
## k      45.36071    9.02675   5.025 6.11e-07 ***
## s       1.46235    0.21493   6.804 1.90e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4524 on 864 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.888e-06
##   (348 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1211     309.99                                 
## 2   1210     309.99   1      0  0.0000    0.9999    
## 3    863     175.99 347    134  1.8935 7.262e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1    3b  8999.426
## 2     4 12724.990
## 3     5 12726.990
## 4     6  8997.414
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.59354    0.46513   1.276 0.202271    
## phi     0.00000    0.01172   0.000 1.000000    
## alpha   0.76837    0.11289   6.806 1.87e-11 ***
## a      24.43593    7.17778   3.404 0.000694 ***
## b      91.93815   13.22793   6.950 7.19e-12 ***
## c     114.37086   17.39595   6.575 8.44e-11 ***
## d       1.22793    0.19996   6.141 1.25e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4516 on 863 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (348 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97047, p-value = 2.825e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.0023, p-value = 1.222e-15
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    408     218.09                                
## 2    407     217.93  1  0.163  0.3045    0.5814    
## 3    383     184.09 24 33.834  2.9330 7.466e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4302.110
## 2     2 4303.803
## 3     3 4088.337
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.32186    0.52276  -0.616    0.538    
## phi    -0.02611    0.02207  -1.183    0.238    
## alpha   0.63678    0.16053   3.967 8.70e-05 ***
## A     190.83546   37.83297   5.044 7.05e-07 ***
## k      52.67803   12.46716   4.225 2.99e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6933 on 383 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.266e-06
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    383     184.09                              
## 2    382     180.46  1  3.637  7.6991 0.005796 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4088.337
## 2    3a 4082.594
## 3    3b 4088.036
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.23186    0.54320  -0.427  0.66973    
## phi    -0.02621    0.02170  -1.207  0.22799    
## alpha   0.62154    0.14827   4.192 3.44e-05 ***
## A     285.12305  130.98147   2.177  0.03011 *  
## k     127.22908   88.65035   1.435  0.15205    
## p       0.04230    0.01344   3.147  0.00178 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6873 on 382 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 8.235e-06
##   (24 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    406     207.53                               
## 2    405     207.47  1  0.063  0.1225   0.7265    
## 3    381     171.16 24 36.312  3.3680 3.26e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 4082.594
## 2     4 4285.720
## 3     5 4287.596
## 4     6 4064.072
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     -0.3922     0.4814  -0.815    0.416    
## phi     0.0000     0.0214   0.000    1.000    
## alpha   0.6720     0.1449   4.637 4.87e-06 ***
## a      24.3767     3.5861   6.798 4.12e-11 ***
## b      78.2867    10.9062   7.178 3.72e-12 ***
## c      56.0639     6.1664   9.092  < 2e-16 ***
## d       0.9506     0.1372   6.928 1.83e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6702 on 381 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (24 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93922, p-value = 1.682e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.7338, p-value = 0.0001886
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    141     88.067                          
## 2    140     88.063  1  0.0038  0.0060 0.9386
## 3    126     75.542 14 12.5205  1.4917 0.1233
##   model      AIC
## 1     1 1555.082
## 2     2 1557.076
## 3     3 1424.171
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.44400    2.00329   0.222   0.8250    
## phi     0.02229    0.04268   0.522   0.6024    
## alpha   1.04434    0.23175   4.506 1.49e-05 ***
## A     182.12937  106.18951   1.715   0.0888 .  
## k      85.27547   57.45271   1.484   0.1402    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7743 on 126 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.842e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 1424.171
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.44400    2.00329   0.222   0.8250    
## phi     0.02229    0.04268   0.522   0.6024    
## alpha   1.04434    0.23175   4.506 1.49e-05 ***
## A     182.12937  106.18951   1.715   0.0888 .  
## k      85.27547   57.45271   1.484   0.1402    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7743 on 126 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.842e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    139     82.744                            
## 2    138     82.744  1   0.00  0.0000 0.99993  
## 3    124     69.784 14  12.96  1.6449 0.07618 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 1424.171
## 2     4 1550.105
## 3     5 1552.105
## 4     6 1417.784
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.248671   2.581509   0.484   0.6295    
## phi    0.008552   0.039876   0.214   0.8305    
## alpha  1.051526   0.227710   4.618 9.55e-06 ***
## a     27.252918  15.017274   1.815   0.0720 .  
## b     51.099738  25.812648   1.980   0.0500 *  
## c     89.540809  37.711187   2.374   0.0191 *  
## d      0.908423   0.492970   1.843   0.0678 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7502 on 124 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87531, p-value = 4.194e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.4376, p-value = 0.0005869
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3966     645.80                                
## 2   3965     639.67  1  6.126  37.974 7.886e-10 ***
## 3   3951     603.74 14 35.932  16.797 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42166.19
## 2     2 42130.36
## 3     3 41805.10
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    9.470e-01  2.122e-01   4.464 8.28e-06 ***
## phi   2.770e-02  4.662e-03   5.941 3.08e-09 ***
## alpha 8.963e-01  6.595e-02  13.590  < 2e-16 ***
## A     3.697e+02  2.607e+01  14.178  < 2e-16 ***
## k     1.712e+02  1.239e+01  13.812  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3909 on 3951 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.688e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3951     603.74                                
## 2   3950     600.51  1 3.2239  21.206 4.255e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 41805.10
## 2    3a 41785.92
## 3    3b 41770.56
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    8.376e-01  2.028e-01   4.129 3.71e-05 ***
## phi   2.518e-02  4.623e-03   5.446 5.46e-08 ***
## alpha 9.234e-01  6.631e-02  13.924  < 2e-16 ***
## A     2.166e+02  1.626e+01  13.321  < 2e-16 ***
## k     6.557e+01  6.665e+00   9.838  < 2e-16 ***
## s     1.361e+00  6.647e-02  20.472  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3892 on 3950 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.404e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3964     637.04                                
## 2   3963     631.93  1  5.106   32.02 1.633e-08 ***
## 3   3949     595.38 14 36.557   17.32 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 41770.56
## 2     4 42116.02
## 3     5 42086.08
## 4     6 41753.95
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    9.106e-01  2.093e-01   4.351 1.39e-05 ***
## phi   2.481e-02  4.607e-03   5.385 7.67e-08 ***
## alpha 9.317e-01  6.524e-02  14.281  < 2e-16 ***
## a     2.114e+01  2.911e+00   7.262 4.58e-13 ***
## b     1.292e+02  8.907e+00  14.504  < 2e-16 ***
## c     1.595e+02  1.517e+01  10.520  < 2e-16 ***
## d     1.410e+00  9.726e-02  14.501  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3883 on 3949 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (14 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98857, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -25.522, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4620     758.87                                
## 2   4619     752.69  1  6.181 37.9323 7.946e-10 ***
## 3   4592     713.21 27 39.481  9.4149 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 51198.35
## 2     2 51162.54
## 3     3 50693.40
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.186629   0.178040   6.665 2.96e-11 ***
## phi    -0.030766   0.004769  -6.451 1.22e-10 ***
## alpha   0.912149   0.061890  14.738  < 2e-16 ***
## A     242.040492  10.235079  23.648  < 2e-16 ***
## k      58.152174   3.131309  18.571  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3941 on 4592 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.32e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   4592     713.21                               
## 2   4591     712.39  1  0.8188  5.2765 0.02166 *  
## 3   4591     708.03  0  0.0000                    
## 4   4590     696.82  1 11.2058 73.8132 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 50693.40
## 2    3a 50690.12
## 3    3b 50661.89
## 4    3c 50590.55
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.382841   0.189176   7.310 3.14e-13 ***
## phi    -0.030859   0.004698  -6.568 5.65e-11 ***
## alpha   0.921594   0.060174  15.316  < 2e-16 ***
## A     149.863516   5.810322  25.793  < 2e-16 ***
## k      38.293455   1.124560  34.052  < 2e-16 ***
## p       0.247314   0.020701  11.947  < 2e-16 ***
## s       2.910487   0.241219  12.066  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3896 on 4590 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.844e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   4618     743.42                             
## 2   4617     743.42  1  0.000   0.000      1    
## 3   4590     702.06 27 41.361  10.015 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 50590.55
## 2     4 51107.25
## 3     5 51109.25
## 4     6 50624.97
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.382841   0.189176   7.310 3.14e-13 ***
## phi    -0.030859   0.004698  -6.568 5.65e-11 ***
## alpha   0.921594   0.060174  15.316  < 2e-16 ***
## A     149.863516   5.810322  25.793  < 2e-16 ***
## k      38.293455   1.124560  34.052  < 2e-16 ***
## p       0.247314   0.020701  11.947  < 2e-16 ***
## s       2.910487   0.241219  12.066  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3896 on 4590 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.844e-06
##   (27 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96958, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -25.3, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    523     64.694                                
## 2    522     62.454  1 2.2402  18.724 1.811e-05 ***
## 3    520     59.006  2 3.4479  15.193 3.868e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5359.324
## 2     2 5342.787
## 3     3 5307.681
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.61595    0.24401  -2.524 0.011890 *  
## phi     0.06602    0.01808   3.652 0.000286 ***
## alpha   0.89778    0.15614   5.750 1.52e-08 ***
## A     338.88585   50.01954   6.775 3.38e-11 ***
## k     100.37823   20.81388   4.823 1.86e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3369 on 520 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.662e-07
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    520     59.006                          
## 2    519     58.894  1 0.11187  0.9859 0.3212
##   model      AIC
## 1     3 5307.681
## 2    3a 5308.684
## 3    3b 5309.018
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.61595    0.24401  -2.524 0.011890 *  
## phi     0.06602    0.01808   3.652 0.000286 ***
## alpha   0.89778    0.15614   5.750 1.52e-08 ***
## A     338.88585   50.01954   6.775 3.38e-11 ***
## k     100.37823   20.81388   4.823 1.86e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3369 on 520 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.662e-07
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    521     64.501                                
## 2    520     62.229  1 2.2721  18.986 1.587e-05 ***
## 3    518     58.912  2 3.3169  14.582 6.900e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 5307.681
## 2     4 5361.749
## 3     5 5344.886
## 4     6 5310.841
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.61595    0.24401  -2.524 0.011890 *  
## phi     0.06602    0.01808   3.652 0.000286 ***
## alpha   0.89778    0.15614   5.750 1.52e-08 ***
## A     338.88585   50.01954   6.775 3.38e-11 ***
## k     100.37823   20.81388   4.823 1.86e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3369 on 520 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.662e-07
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96189, p-value = 2.028e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5579, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    586     115.11                                
## 2    585     115.11  1 0.0005  0.0027    0.9589    
## 3    582     110.92  3 4.1918  7.3318 7.868e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6079.429
## 2     2 6081.427
## 3     3 6047.977
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.572496   0.608073   0.941 0.346843    
## phi    -0.008085   0.017953  -0.450 0.652630    
## alpha   0.882103   0.230491   3.827 0.000144 ***
## A     473.611228 148.437249   3.191 0.001496 ** 
## k     254.538269  86.216611   2.952 0.003281 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4366 on 582 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.3e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    582     110.92                         
## 2    581     110.62  1 0.2994  1.5726 0.2103
##   model      AIC
## 1     3 6047.977
## 2    3a 6048.391
## 3    3b 6915.692
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.572496   0.608073   0.941 0.346843    
## phi    -0.008085   0.017953  -0.450 0.652630    
## alpha   0.882103   0.230491   3.827 0.000144 ***
## A     473.611228 148.437249   3.191 0.001496 ** 
## k     254.538269  86.216611   2.952 0.003281 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4366 on 582 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.3e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    584     114.44                                
## 2    583     114.43  1 0.0054  0.0274    0.8685    
## 3    580     110.29  3 4.1401  7.2574 8.728e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6047.977
## 2     4 6079.986
## 3     5 6081.958
## 4     6 6048.664
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.572496   0.608073   0.941 0.346843    
## phi    -0.008085   0.017953  -0.450 0.652630    
## alpha   0.882103   0.230491   3.827 0.000144 ***
## A     473.611228 148.437249   3.191 0.001496 ** 
## k     254.538269  86.216611   2.952 0.003281 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4366 on 582 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.3e-06
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96323, p-value = 5.971e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.5051, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    308     94.545                          
## 2    307     94.155   1   0.39  1.2728 0.2601
## 3    149     49.395 158  44.76  0.8545 0.8349
##   model      AIC
## 1     1 3309.570
## 2     2 3310.284
## 3     3 1658.712
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge     -1.43647    1.51047  -0.951   0.3431  
## phi     0.02004    0.04933   0.406   0.6851  
## alpha   0.74585    0.28704   2.598   0.0103 *
## A     193.80924  139.40676   1.390   0.1665  
## k      12.32409   10.64052   1.158   0.2486  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5758 on 149 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 7.773e-06
##   (158 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    149     49.395                          
## 2    148     49.191  1 0.20423  0.6145 0.4344
##   model      AIC
## 1     3 1658.712
## 2    3a 1660.074
## 3    3b 1648.175
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.626861   1.205601  -1.349    0.179    
## phi     0.008848   0.048243   0.183    0.855    
## alpha   0.587047   0.318116   1.845    0.067 .  
## A     189.493730 117.280510   1.616    0.108    
## k      40.017398   0.670930  59.645   <2e-16 ***
## s      63.679888 108.268749   0.588    0.557    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5547 on 148 degrees of freedom
## 
## Number of iterations to convergence: 19 
## Achieved convergence tolerance: 6.42e-06
##   (158 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)  
## 1    306     91.857                             
## 2    305     91.040   1  0.818  2.7388 0.09897 .
## 3    147     47.591 158 43.449  0.8494 0.84325  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 1648.175
## 2     4 3304.600
## 3     5 3303.820
## 4     6 1656.982
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.626861   1.205601  -1.349    0.179    
## phi     0.008848   0.048243   0.183    0.855    
## alpha   0.587047   0.318116   1.845    0.067 .  
## A     189.493730 117.280510   1.616    0.108    
## k      40.017398   0.670930  59.645   <2e-16 ***
## s      63.679888 108.268749   0.588    0.557    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5547 on 148 degrees of freedom
## 
## Number of iterations to convergence: 19 
## Achieved convergence tolerance: 6.42e-06
##   (158 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98431, p-value = 0.0781
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.0021003, p-value = 0.9983
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    247    102.693                          
## 2    246    102.569  1  0.1246  0.2990 0.5850
## 3    175     77.963 71 24.6053  0.7779 0.8865
##   model      AIC
## 1     1 2514.590
## 2     2 2516.287
## 3     3 1829.728
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.336427   1.519780  -0.221  0.82507    
## phi    -0.004472   0.040339  -0.111  0.91185    
## alpha   0.772198   0.213500   3.617  0.00039 ***
## A     110.544511  48.539478   2.277  0.02397 *  
## k      50.619975  25.176162   2.011  0.04590 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6675 on 175 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.61e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)
## 1    175     77.963                           
## 2    211     86.584 -36 -8.6205  0.5375 0.9851
## 3    174     77.438  37  9.1463  0.5554 0.9817
## 4    210     86.173 -36 -8.7353  0.5452 0.9832
##   model      AIC
## 1     3 1829.728
## 2    3a 2170.479
## 3    3b 1830.510
## 4    3c 2171.446
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.336427   1.519780  -0.221  0.82507    
## phi    -0.004472   0.040339  -0.111  0.91185    
## alpha   0.772198   0.213500   3.617  0.00039 ***
## A     110.544511  48.539478   2.277  0.02397 *  
## k      50.619975  25.176162   2.011  0.04590 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6675 on 175 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.61e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    245    102.324                         
## 2    244    102.324  1   0.00  0.0000 1.0000
## 3    173     77.733 71  24.59  0.7708 0.8945
##   model      AIC
## 1     3 1829.728
## 2     4 2517.688
## 3     5 2519.688
## 4     6 1833.196
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.336427   1.519780  -0.221  0.82507    
## phi    -0.004472   0.040339  -0.111  0.91185    
## alpha   0.772198   0.213500   3.617  0.00039 ***
## A     110.544511  48.539478   2.277  0.02397 *  
## k      50.619975  25.176162   2.011  0.04590 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6675 on 175 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.61e-06
##   (74 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93026, p-value = 1.295e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.5617, p-value = 0.0003684
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 3b 6 6
212 Laurentian Mixed Forest 3c 6 6
221 Eastern Broadleaf Forest 3b 6 6
222 Midwest Broadleaf Forest 3a 6 6
223 Central Interior Broadleaf Forest 3b 6 6
231 Southeastern Mixed Forest 3c 6 6
232 Outer Coastal Plain Mixed Forest 3c 6 6
234 Lower Mississippi Riverine Forest 3 3 3
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 3b 6 6
255 Prairie Parkland (Subtropical) 3a 6 6
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA NA NA
313 Colorado Plateau Semi-Desert NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe NA NA NA
332 Great Plains Steppe 3 6 6
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3b 6 6
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3c 3c 3c
M223 Ozark Broadleaf Forest Meadow 3 3 3
M231 Ouachita Mixed Forest 3 3 3
M242 Cascade Mixed Forest NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3b 3b 3b
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M334 Black Hills Coniferous Forest 3 3 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA NA NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.se b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.6301633 0.0478700 0.2011991 1.0591274 0.0169332 0.0000322 0.0058101 0.0280563 1.1697903 0.0046962 1.0354324 1.3041482 313.9973 224.90265 403.0919 103.10784 57.3911644 148.82451 38.93749 34.564842 43.31014 112.24482 NA 99.8673859 124.62226 116.17018 104.95394 127.38642 0.9314725 0.8278628 1.035082
212 Laurentian Mixed Forest east 12962 6481 0.1808888 0.0234806 -0.1194899 0.4812674 0.0211932 0.0000203 0.0123708 0.0300155 0.9083255 0.0018663 0.8236415 0.9930094 124.8983 112.63007 137.1665 45.82483 41.9172456 49.73240 23.57869 21.015035 26.14235 86.44570 NA 78.8333156 94.05809 125.36219 111.21370 139.51068 1.3509549 1.2283128 1.473597
221 Eastern Broadleaf Forest east 5446 2723 0.6042574 0.0295961 0.2669821 0.9415327 0.0000000 0.0000197 -0.0086968 0.0086968 0.9247621 0.0026719 0.8234238 1.0261003 269.2999 226.45981 312.1400 61.79384 48.5722847 75.01539 27.90799 21.840874 33.97510 151.78054 NA 134.6780153 168.88306 133.03954 112.19473 153.88434 1.3181621 1.1569422 1.479382
222 Midwest Broadleaf Forest east 3552 1776 -0.3019439 0.0650521 -0.8021219 0.1982342 0.0457054 0.0001683 0.0202607 0.0711502 0.9776442 0.0055842 0.8310980 1.1241904 415.2918 291.42919 539.1544 145.60494 82.6853980 208.52448 25.34285 20.338823 30.34688 125.49277 NA 107.9061657 143.07938 105.73419 91.72965 119.73874 1.0355867 0.8961121 1.175061
223 Central Interior Broadleaf Forest east 6388 3194 -0.0887126 0.0180864 -0.3523746 0.1749494 0.0000000 0.0000392 -0.0122715 0.0122715 0.8518000 0.0031221 0.7422544 0.9613455 187.6025 165.85945 209.3455 40.38205 34.4914196 46.27268 29.94935 24.307638 35.59107 116.92794 NA 106.3505886 127.50530 104.05768 92.83703 115.27834 1.2094471 1.0687829 1.350111
231 Southeastern Mixed Forest east 7790 3895 1.5684019 0.0344772 1.2044010 1.9324028 0.0000000 0.0000216 -0.0091043 0.0091043 0.8342246 0.0021963 0.7423523 0.9260969 159.4438 142.63460 176.2530 34.73307 30.9341582 38.53197 16.88756 13.676656 20.09847 127.95402 NA 112.9401111 142.96793 137.97548 105.68394 170.26702 1.7878677 1.5849700 1.990765
232 Outer Coastal Plain Mixed Forest east 7940 3970 1.0398178 0.0414701 0.6406081 1.4390274 0.0109689 0.0000289 0.0004379 0.0215000 0.8062593 0.0019510 0.7196702 0.8928484 161.5742 142.76226 180.3861 36.06069 31.9700715 40.15132 21.48141 17.892126 25.07070 129.35806 NA 112.0857189 146.63040 136.70672 102.42869 170.98475 1.6721462 1.4578732 1.886419
234 Lower Mississippi Riverine Forest east 830 415 0.0548083 0.2309309 -0.8888094 0.9984260 0.0265263 0.0003264 -0.0089483 0.0620009 0.8914939 0.0107605 0.6878037 1.0951842 622.1739 329.30518 915.0427 187.66098 86.9903041 288.33166 NA NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.5935419 0.2163450 -0.3193746 1.5064584 0.0000000 0.0001373 -0.0230016 0.0230016 0.7683654 0.0127436 0.5467994 0.9899313 151.4269 102.96746 199.8864 45.36071 27.6437845 63.07764 24.43593 10.347990 38.52387 91.93815 NA 65.9754728 117.90083 114.37086 80.22754 148.51418 1.2279330 0.8354607 1.620405
255 Prairie Parkland (Subtropical) east 444 222 -0.3921693 0.2317805 -1.3387733 0.5544348 0.0000000 0.0004578 -0.0420678 0.0420678 0.6719871 0.0210045 0.3870259 0.9569483 285.1230 27.58813 542.6580 127.22908 -47.0746672 301.53282 24.37674 17.325824 31.42766 78.28675 NA 56.8429742 99.73053 56.06386 43.93946 68.18827 0.9505804 0.6808014 1.220360
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 1.2486710 6.6641900 -3.8608589 6.3582010 0.0085525 0.0015901 -0.0703735 0.0874784 1.0515265 0.0518519 0.6008244 1.5022286 182.1294 -28.01655 392.2753 85.27547 -28.4217543 198.97270 27.25292 -2.470473 56.97631 51.09974 NA 0.0092781 102.19020 89.54081 14.89981 164.18181 0.9084226 -0.0673038 1.884149
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 0.9106063 0.0437947 0.5003152 1.3208974 0.0248077 0.0000212 0.0157755 0.0338399 0.9317467 0.0042567 0.8038335 1.0596599 216.5856 184.70893 248.4623 65.57398 52.5065750 78.64139 21.13968 15.432210 26.84715 129.19346 NA 111.7300914 146.65682 159.54583 129.81340 189.27826 1.4103995 1.2197164 1.601082
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 1.3828406 0.0357875 1.0119648 1.7537165 -0.0308590 0.0000221 -0.0400697 -0.0216484 0.9215941 0.0036209 0.8036248 1.0395634 149.8635 138.47249 161.2545 38.29346 36.0887776 40.49813 NA NA NA NA NA NA NA NA NA NA NA NA NA
M223 Ozark Broadleaf Forest Meadow east 602 301 -0.6159480 0.0595402 -1.0953117 -0.1365842 0.0660238 0.0003268 0.0305091 0.1015385 0.8977772 0.0243786 0.5910414 1.2045130 338.8858 240.62063 437.1511 100.37823 59.4885909 141.26786 NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 680 340 0.5724965 0.3697528 -0.6217884 1.7667813 -0.0080849 0.0003223 -0.0433450 0.0271752 0.8821030 0.0531259 0.4294083 1.3347977 473.6112 182.07329 765.1492 254.53827 85.2046721 423.87187 NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 330 165 -1.6268614 1.4534734 -4.0092764 0.7555535 0.0088479 0.0023274 -0.0864860 0.1041818 0.5870475 0.1011980 -0.0415895 1.2156844 189.4937 -42.26693 421.2544 40.01740 38.6915584 41.34324 NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 306 153 -0.3364271 2.3097314 -3.3358839 2.6630297 -0.0044724 0.0016272 -0.0840860 0.0751412 0.7721982 0.0455825 0.3508309 1.1935654 110.5445 14.74639 206.3426 50.61997 0.9319872 100.30796 NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot phi (effect of DeltaPDSI)

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 19 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 19 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region  weighted.ge weighted.ge.std_Error 95 % CI, upper
## 1     entire US  0.616733834           0.061620764    0.737510532
## 2       pacific -0.008358986           0.006194505    0.003782243
## 3          east  0.623701660           0.060564028    0.742407156
## 4 interior west  0.001391160           0.009526026    0.020062171
##   95 % CI, lower
## 1     0.49595714
## 2    -0.02050022
## 3     0.50499617
## 4    -0.01727985

phi (effect of DeltaPDSI)

##          region  weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  9.838444e-03           5.743138e-08   9.838557e-03
## 2       pacific  4.546141e-05           7.718904e-09   4.547654e-05
## 3          east  9.793784e-03           5.651635e-08   9.793895e-03
## 4 interior west -8.014508e-07           6.684597e-09  -7.883490e-07
##   95 % CI, lower
## 1   9.838332e-03
## 2   4.544628e-05
## 3   9.793674e-03
## 4  -8.145526e-07

alpha (biomass compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.897805788             5.423982e-07    0.897806851
## 2       pacific    0.003016312             5.089888e-08    0.003016412
## 3          east    0.888589063             5.388067e-07    0.888590119
## 4 interior west    0.006200413             3.595057e-08    0.006200483
##   95 % CI, lower
## 1    0.897804725
## 2    0.003016212
## 3    0.888588007
## 4    0.006200342

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   205.3828
## 2       pacific   169.9264
## 3          east   206.6700
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   59.87703
## 2       pacific   35.88517
## 3          east   60.16440
## 4 interior west   45.14532

Model Bookeeping

1. Delta-B due to Delta-STDAGE

2. Delta-B due to Delta-Year (ge)

make a fig

## Warning: Removed 10138 rows containing missing values (geom_point).

3. stand age densities

make a fig

## Picking joint bandwidth of 7.36